Jalal Talabani has designated Jawad al-Maliki, a Shi'ite, as prime minister and asked him to form a government.
The move Saturday breaks a four month political impasse over naming a new prime minister.
President Bush hailed it as a historic achievement that will make America, as well as Iraq, more secure. He said the agreement represents compromise and the will of the Iraqi people.
Earlier, U.S. Secretary of State Condoleezza Rice today called it an "important milestone".
Mr. Talabani made the announcement during a parliament session that approved several nominations for government posts.
In the session, Mr. Talabani, a Kurd, was elected to another term as president, while a Sunni Arab, Mahmoud al-Mashhadani, was elected parliament speaker.
In other developments, the U.S. military announced the deaths of five U.S. soldiers, including four who were killed Saturday by a roadside bomb south of Baghdad.
It said the fifth soldier also died from a roadside bomb south of Baghdad, but did not specify if it was the same attack that killed the others.
Elsewhere, two people were killed and at least 10 others wounded when two roadside bombs exploded within minutes of each other near Baquba.
Information for this report is perovided by AP.